By (REF ), the scattering dyadic transforms an incident spectrum of plane waves described by the vector function \(Ḙ_0({r}^{\prime })\)  into the scattered far field \(F̭({r})\)  analogously to how a transition matrix transforms regular spherical waves into outgoing spherical waves [1]} or an admittance matrix transforms incident electric field into induced electric currents [2]}. As such, an eigenvalue decomposition of the scattering dyadic can be used to generate eigenfunctions \(F̭_n\) , which, when applied as incident fields, produce scattered fields with the same pattern, ,
\(\int \limits _{4\pi } S̭({r},{r}^{\prime }) \cdot F̭_n({r}^{\prime }) ^{\prime } = t_n F̭_n({r}).\) 
